Broadband transmission line models for analysis of serial data channel interconnects Simberian: Advanced, Easy-to-Use and Affordable Electromagnetic Solutions… Y. O. Shlepnev, Simberian, Inc. [email protected]PCB Design Conference East, Durham NC, October 23, 2007
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Broadband transmission line models for analysis of serial data
channel interconnects
Simberian: Advanced, Easy-to-Use and Affordable Electromagnetic Solutions…
IntroductionFaster data rates drive the need for accurate electromagnetic models for multi-gigabit data channelsWithout the electromagnetic models, a channel design may require
Test boards, experimental verification, … Multiple iterations to improve performance
No models or simplified static models may result in the design failure, project delays, increased cost …
Since 90-s Static field solvers for parameters extraction, frequency-dependent analytical loss modelsW-element for line segment analysis
Trends in this decadeTransition to full-wave electromagnetic field solversMethod of characteristic type algorithms or W-elements with tabulated RLGC per unit length parameters for analysis of line segment
Broadband characteristic impedance and propagation constant for a simple strip-line
( )0Re Z
( )0Re Z
( ) ( ) ( )0Z Z Yω ω ω=
( ) ( ) ( )Z Y iω ω ω α βΓ = ⋅ = +
Frequency, Hz Frequency, Hz
Attenuation Constant [Np/m]
Phase Constant [rad/m]
Complex characteristic impedance [Ohm]
8-mil strip, 20-mil plane to plane distance. DK=4.2, LT=0.02 at 1 GHz, no dielectric conductivity. Strip is made of copper, planes are ideal, no roughness, no high-frequency dispersion.
Via-hole transitions and discontinuities:Reflection, radiation and impedance mismatch
Transmission lines: Attenuation and dispersion due to physical conductor and dielectric propertiesHigh-frequency dispersion
Dispersion
Attenuation
Reflection
Presenter
Presentation Notes
Signal degradation factors can be formally separated into two groups. First, degradation in the straight segment of transmission line caused by losses and dispersion due to dielectric and conductor properties and high-frequency dispersion. Two graphs on the right illustrate typical dependencies of attenuation and delays p.u.l. for a PCB line. Second, discontinuities or transitions such as via-holes reflect the signal and electrically couple signal to parallel-plane structures and space around the board.
proximity and edge-effects or transition to skin-effect ~1 MHz or higher
well-developed skin-effect ~100 MHz or higher
Resi
stan
ce p
.u.l
. R
(f)
incr
ease
s
Roughness ~40 MHz
DC
uniform current distribution
dispersion and edge effects – further degradation
Low
Med
ium
Hig
h
R(f) and L(f) increase
Frequency
y yE Jρ=Hz
( )1expy s
s
iJ J x
δ− +⎛ ⎞
= ⋅ ⎜ ⎟⎝ ⎠
ZX
Y
Skin-effect
[ ]s mf
ρδπμ
=
Presenter
Presentation Notes
Let’s take a closer look at the degradation effects related to the conductor properties. At low frequencies the current distribution is uniform across the traces and planes and at about 10 KHz current in plane concentrates below the strip. At the medium frequencies we observe a transition to skin-effect and current becomes larger near the conductor surface and near the corners. Finally, at high frequencies, current inside the conductors is almost zero and we can talk about well-developed skin-effect. Transition from low to high frequencies causes increase of R p.u.l. and decrease of L p.u.l. due to larger current near surface and smaller magnetic field energy inside the conductor. If skin depth becomes comparable with the surface roughness, the roughness causes increase of both R and L. Dispersion due to presence of dielectric and edge-effect at high frequencies can case further changes in R and L. Picture on the left illustrates the skin-effect as the energy absorption by a conductor. Energy flows inside the conductor and not along the wave propagation direction.
To quantify the medium frequencies or transition to skin-effect we can use either thickness of strip or plane to skin depth ratio (t/s) or equality of the real and imaginary parts of the internal impedance p.u.l. This is example of current density and internal impedance for a 10 mil by 1 mil strip. At thickness to skin depth 0.5, the current distribution is uniform and the imaginary part of the internal impedance is less than 5% of the real part. When the strip thickness becomes 2 skin depth at 28 MHz, the ratio of current density in the center to the current density at the edge is still high – 0.76, and the real and imaginary parts are not close to each other. Only at 170 MHz, when strip is 5 skin-depth thick, current in the center is relatively low and the difference between the real and imaginary parts of the impedance is a few %.
Transition from 0.5 skin depth to 2 and 5 skin depths for copper interconnects on PCB, Package, RFIC and IC
Interconnect or plane thickness in micrometers vs. Frequency in GHz
RFIC
Package
IC
No skin-effect
Well-developed skin-effect
PCB
Ratio of skin depth to r.m.s. surface roughness in micrometers vs. frequency in GHz
Roughness has to be accounted if rms value is comparable with the skin depth
Presenter
Presentation Notes
Now we can defined the medium frequencies for different technologies on the base of the strip or plane thickness to skin depth ratio. The vertical axis on the left graph is conductor thickness in micrometers. The horizontal axis is frequency. Along the blue line the conductor thickness is half of skin depth and there no skin-effect below this line. Along red line, the conductor thickness is equal to five skin depth. Well-developed skin-effect area is above the red line. Transition to skin-effect occurs between those lines. We can see that different technologies may have transition at different frequencies. Conductor thickness for PCB technology may be from 50 um to 15 um. It means that transition frequencies may be as high as 500 MHz. With 5 um conductor thickness in packaging applications, the transition takes place from 40 MHz to 4 GHz – right in the middle of serdes spectrum. With 2 um thickness the transition takes place at 20 GHz. In addition, the conductor surface roughness can complicate the analysis. It must be accounted as soon as root mean square of the bumps is about one skin-depth. With 10 um roughness it means frequencies as low as 40 MHz, where the roughness can substantially change the attenuation. Typical PCBs or packaging applications may have roughness from 5 to 1 um, that is in the frequency band relevant to the serdes interconnects analysis. Note that this classification is necessary only to understand the limitations of a particular solver. A static solver for instance always assumes well developed skin effect to estimate the resistance and internal inductance p.u.l. Simbeor does not have restrictions in analysis of the conductor effects.
Dielectric attenuation and dispersion effectsDispersion of complex dielectric constant
Polarization changes with frequencyHigh frequency harmonics propagate fasterAlmost constant loss tangent in broad frequency range – loss ~ frequency
High-frequency dispersion due to non-homogeneous dielectrics
TEM mode becomes non-TEM at high frequenciesFields concentrate in dielectric with high Dk or lower LTHigh-frequency harmonics propagate slowerInteracts with the conductor-related losses
Dielectric effects can technically be separated into two parts. The first one is related to the frequency-dependent polarization or dielectric property itself. Typical dependency of dielectric constant for FR4-type dielectrics is shown here. Dielectric constant decrease with the frequency and loss tangent is zero a DC, grows to some values, slowly grows over a wide frequency band and drops to zero at extremely high frequencies. Such causal wideband Debye model can be constructed from just one frequency measurement. Higher frequency harmonics propagate faster due to the dielectric constant decrease. Another phenomenon related to non-homogeneous dielectric is concentration of electromagnetic field in the dielectric with higher dielectric constant as illustrated here. TEM modes become non-TEM due to the longitudinal components of electromagnetic field. Full-wave analysis is required to simulate this effect. Higher frequency harmonics propagate slower and L p.u.l. increases. Technically the high-frequency dispersion is not separable from the conductor effects and usually increases the losses p.u.l.
2D Static and Magneto-Quasi-Static Solvers 3D Full-Wave Solver
E i H
H i E E J
ωμ
ωε σ
∇× = −
∇× = + +
2D Full-Wave Solvers
System-level simulator
( )( )
exp
expt
t
E E l
H H l
= ⋅ −Γ ⋅
= ⋅ −Γ ⋅
Presenter
Presentation Notes
A system-level solver is usually used to do the analysis of either chip-to-chip channel or a board portion of the channel. Eldo, HSPICE, ADS can be used for instance. The models of the interconnects produces by electromagnetic solvers. Static or quasi-static solvers are usually used to extract t-line parameters for W-element. We suggest to use one 3-D solver for extraction of both frequency-dependent RLGC parameters per unit length for t-lines.
Plus additional boundary conditions at the boundaries between dielectrics
Solve Laplace’s equations for a transmission line cross-section to find capacitance and conductance p.u.l. matrices and distribution or charge on metal boundaries
Integral equation or boundary element methods with meshing of conductor and dielectric boundaries are usually used to solve the problem.
Conductor loss accounted for with diagonal RDC and with R computed at 1 GHz with the perturbation method, assuming well-developed skin effect
Frequency-dependent impedance p.u.l. model based on static solution
DCR
8-mil strip, 20-mil plane to plane distance. DK=4.2, LT=0.02 at 1 GHz, no dielectric conductivity. Strip is made of copper, planes are ideal, no roughness no high-frequency dispersion.
A x y i A A insideconductorsA x y outsideconductors
ωσμ∇ = ⋅ −∇ =
Plus additional boundary conditions at the conductor surfaces
Solve Laplace’s equations outside of the conductors simultaneously with diffusion equations inside the conductors to find frequency-dependent resistance and inductance p.u.l.
( )( )R fL f
•Finite Element Method meshes whole cross-section of t-line including the metal interior
•Integral Equation Method can be used to mesh just the interior of the strips and planes
•Both approaches have significant numerical complexity (despite on being 2D):•To extract parameters of a line up to 10 GHz, the element or filament size near the metal surface has to be at least ¼ or skin depth that is about 0.16 um
•It would be required about 236000 elements to mesh interior of 10 mil by 1 mil trace for instance and in addition interior of one or two planes have to be meshed too (another two million elements may be required)
•If element size is larger than skin-depth, effect of saturation of R can be observed (R does not grow with frequency)
•In addition, there is no influence of dielectric on the extracted R and L
Solve Maxwell’s equations for a transmission line segment to find S-parameters and frequency-dependent matrix RLGC per unit length parameters:
Plus additional boundary conditions at the metal and dielectric surfaces
( )( ) ( )( ) ( )
,,,
S lR LG C
ωω ωω ω
l
1 2 N
N+1 2N
Method of Lines (MoL) for multilayered dielectricsHigh-frequency dispersion in multilayered dielectricsLosses in metal planesCausal wideband Debye dielectric polarization loss and dispersion models
Trefftz Finite Elements (TFE) for metal interiorMetal interior and surface roughness models to simulate proximity edge effects, transition to skin-effect and skin effect
Method of Simultaneous Diagonalization (MoSD) for lossy multiconductor line and multiport S-parameters extraction
Advanced 3-D extraction of modal and RLGC(f) p.u.l. parameters of lossy multi-conductor lines
Effect of skin-effect in thin plane on a PCB differential microstrip line
Effect of Dispersion
Skin Effects in thin plane
Differential mode impedance
Common mode impedance
Attenuations
7.5 mil wide 2.2 mil thick strips 20 mil apart. Dielectric substrate with Dk=4.1 and LT=0.02 at 1 GHz. Substrate thickness 4.5 mil, plane thickness 0.594 mil, metal surface roughness 0.5 um
Eye diagram comparison for 5-inch differential micro-strip line segment with 20 Gbs data rate
Two 7.5 mil traces 20 mil apart on 4.5 mil dielectric and 0.6 mil plane, 0.5 um roughness. Worst case eye diagram for 50 ps bit interval – May affect channel budget!
Worst case eye diagram computed with W-element defined with tabulated RLGC parameters extracted with Simbeor
Worst case eye diagram computed with W-element defined with t-line parameters extracted with a static solver
Transition to skin-effect and roughness in a package strip-line
Rough
FlatTransition to skin-effect Rough
FlatLossless
Lossy
79 um wide and 5 um thick strip in dielectric with Dk=3.4. Distance from strip to the top plane 60 um, to the bottom plane 138 um. Top plane thickness is 10 um, bottom 15 um. RMS roughness is 1 um on bottom surface and almost flat on top surface of strip, RMS roughness factor is 2.33% loss increase at 10 GHz
Effect of metal surface finish on a PCB microstrip line parameters
NoFinish – 8 mil microstrip on 4.5 mil dielectric with Dk=4.2, LT=0.02 at 1 GHz. ENIG2 - microstrip surface is finished with 6 um layer of Nickel and 0.1 um layer of gold on topNickel resistivity is 4.5 of copper, mu is 10
Conclusion – Select the right tool to build broadband transmission line models
Use broadband and causal dielectric modelsSimulate transition to skin-effect, shape and proximity effects at medium frequenciesAccount for skin-effect, dispersion and edge effect at high frequenciesHave conductor models valid and causal over 5-6 frequency decades in generalAccount for conductor surface roughness and finishAutomatically extract frequency-dependent modal and RLGC matrix parameters per unit length for W-element models of multiconductor lines
BiographyYuriy Shlepnev is the president and founder of Simberian Inc., were he develops electromagnetic software for electronic design automation. He received M.S. degree in radio engineering from Novosibirsk State Technical University in 1983, and the Ph.D. degree in computational electromagnetics from Siberian State University of Telecommunications and Informatics in 1990. He was principal developer of a planar 3D electromagnetic simulator for Eagleware Corporation. From 2000 to 2006 he was a principal engineer at Mentor Graphics Corporation, where he was leading the development of electromagnetic software for simulation of high-speed digital circuits. His scientific interests include development of broadband electromagnetic methods for signal and power integrity problems. The results of his research published in multiple papers and conference proceedings.